Coombs Ex.19 full — STAR: Boone wins the runoff 8–7¶

Generated from bv2165_9vxcj7_star.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: STAR (single winner) · 1 seat · Expected winner: Boone

▶ Live on BetterVoting: vote · results ↗ (election 9vxcj7 · test BV2165).

Scenario¶

Race 1 of 2 in the Coombs No-Show pair, part 1 of 2 (BV2165, bvid 9vxcj7; BV-confirmed; the pair is BV2165/66). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A7 (Coombs' procedure), Example 19. The full electorate: 15 voters — 4×(Amy>Boone>Cass), 4×(Boone>Cass>Amy), 5×(Cass>Amy>Boone), 2×(Cass>Boone>Amy). Coombs (worked on the case page; no tabulator on BV or in LH): Amy is ranked last by the most voters (6) and is deleted; Boone then holds a majority — Boone wins. This STAR race (5/3/1 map): Amy 41, Boone 43, Cass 51 — Cass tops the scores, but Boone wins the automatic runoff 8–7. Part 2 (BV2166): the two Cass>Boone>Amy voters stay home, and BOTH Coombs and STAR flip to Cass, their favorite. Pairwise is a cycle (Amy>Boone 9–6, Boone>Cass 8–7, Cass>Amy 11–4) — no RR race; IRV's first elimination is a random Amy/Boone tie — no IRV race. Live results: https://bettervoting.com/9vxcj7/results

Ballots¶

Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).

Amy,Boone,Cass
5,3,1
5,3,1
5,3,1
5,3,1
1,5,3
1,5,3
1,5,3
1,5,3
3,1,5
3,1,5
3,1,5
3,1,5
3,1,5
1,3,5
1,3,5

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

[Divergence from STAR]
  STAR                   = Boone
  Choose-One (Plurality) = Cass   (differs from STAR)
  Approval               = Cass   (differs from STAR)
  RCV-RR                 = Cass   (differs from STAR)
  Full round-by-round reports (generated for review):
  RCV-RR round-robin: cases_tabulated/bv2165_9vxcj7_star_RCV-RR_tabulated.txt

[Runoff Reversal]
 - Score Round Winner(s) = (Cass)
 - Runoff Round Winner   = (Boone)
  Candidate Cass earned the highest total score, but
  Candidate Boone won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 15 ballots.
Count × Amy,Boone,Cass
    5 ×   3,    1,   5
    4 ×   5,    3,   1
    4 ×   1,    5,   3
    2 ×   1,    3,   5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Cass          -- 51 -- First place
   Boone         -- 43 -- Second place
   Amy           -- 41
 Cass and Boone advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Boone         -- 8 -- First place
   Cass          -- 7
   Equal Support -- 0
 Boone wins.
   Runoff math:
     15  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     15  voters with a preference  (majority = 8)
           Boone 8 (53%)  ·  Cass 7 (47%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Boone

Full audit — preference matrix, Condorcet, and score distribution¶

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |      Amy     |  * Boone    |   * Cass    |
-------------------------------------------------------------
           Amy > |     ---      | 9 -  0 -  6 | 4 -  0 - 11 |
       * Boone > |  6 -  0 -  9 |    ---      | 8 -  0 -  7 |
        * Cass > | 11 -  0 -  4 | 7 -  0 -  8 |    ---      |

[Condorcet Winner]
  No Condorcet winner (majority cycle: Amy > Boone > Cass > Amy)

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Amy        4  0  5  0  6  0  |    41   2.7
Boone      4  0  6  0  5  0  |    43   2.9
Cass       7  0  4  0  4  0  |    51   3.4

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/felsenthal_paradoxes/cases/bv2165_9vxcj7_star.yaml

See also¶

Methods disagree on this election — its entry in the divergence review ledger
Condorcet efficiency (topic hub)
Ties & tie-breaking (topic hub)
Runoff reversal (worked set)
Glossary · all cases by method